Problem: $f(t) = (22t, 33\sin(3t))$ What is the velocity of $f(t)$ ? Choose 1 answer: Choose 1 answer: (Choice A) A $(22, 33\cos(3t))$ (Choice B) B $\sqrt{22^2+33^2\sin^2(3t)}$ (Choice C) C $(22, 99\cos(3t))$ (Choice D) D $\sqrt{22^2+99^2\cos^2(3t)}$
Solution: The velocity of a parametric curve is the derivative of its position. If $f(t) = (a(t), b(t))$, then the velocity is: $f'(t) = (a'(t), b'(t))$ Our position function here is $f(t)$. $f'(t) = (22, 99\cos(3t))$ Therefore, the velocity of $f(t)$ is $(22, 99\cos(3t))$.